Håkan Andréasson

Reduction of barnacle recruitment on micro‐textured surfaces: Analysis of effective topographic characteristics and evaluation of skin friction

This study investigates five designed micro‐textured surfaces and their effects on barnacle fouling and hydrodynamic drag. Three of the micro‐textures were developed in the present study and evaluated together with two commercial riblet films. All micro‐structures were arranged as longitudinal grooves with different profile depths, widths and angles of inclination. In field tests the recruitment of the barnacle Balanus improvisus on micro‐textured surfaces and smooth controls was evaluated. All micro‐textured surfaces reduced recruitment, and the most efficient texture reduced recruitment by 98%. For some micro‐textures the reduction of recruitment declined as settlement intensity increased. In a correlative analysis, the trigonometric inclination of the micro‐structures explained most of the recruitment reduction. The steepest angle of inclination caused a massive reduction in barnacle settlement. Surface micro‐structures may affect the boundary‐layer flow and the hydrodynamic drag (skin friction) of the surface. The skin friction was empirically measured in a flow channel using a sub‐set of the tested micro‐textures. The measurements of skin friction showed that the orientation of the microstructures is important, with a minimum friction when the grooves are parallel to the flow. For one of the micro‐textures the skin friction was ca 10% lower compared to a hydraulically smooth surface. It is concluded that, depending on the flow speed, micro‐textures will not significantly increase skin friction when arranged parallel to the flow, even at moderate protrusion through the viscous sub‐layer.

Sharp bounds on 2m/r of general spherically symmetric static objects

In 1959 Buchdahl [H.A. Buchdahl, General relativistic fluid spheres, Phys. Rev. 116 (1959) 1027-1034] obtained the inequality 2 M / R ≤ 8 / 9 under the assumptions that the energy density is non-increasing outwards and that the pressure is isotropic. Here M is the ADM mass and R the area radius of the boundary of the static body. The assumptions used to derive the Buchdahl inequality are very restrictive and for instance neither of them hold in a simple soap bubble. In this work we remove both of these assumptions and consider any static solution of the spherically symmetric Einstein equations for which the energy density ρ ≥ 0, and the radial and tangential pressures p ≥ 0 and pT satisfy p + 2 pT ≤ Ω ρ, Ω > 0, and we show thatunder(sup, r > 0) frac(2 m (r), r) ≤ frac((1 + 2 Ω)2 - 1, (1 + 2 Ω)2), where m is the quasi-local mass, so that in particular M = m (R). We also show that the inequality is sharp under these assumptions. Note that when Ω = 1 the original bound by Buchdahl is recovered. The assumptions on the matter model are very general and in particular any model with p ≥ 0 which satisfies the dominant energy condition satisfies the hypotheses with Ω = 3.

Global Foliations of Matter Spacetimes¶with Gowdy Symmetry

Abstract:A global existence theorem, with respect to a geometrically defined time, is shown for Gowdy symmetric globally hyperbolic solutions of the Einstein–Vlasov system for arbitrary (in size) initial data. The spacetimes being studied contain both matter and gravitational waves.

On the Einstein-Vlasov system with hyperbolic symmetry

It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discussed.

Regularity of the gain term and strong L 1 convergence to equilibrium for the relativistic Boltzmann equation

The main purpose of the paper is to show that the gain term of the relativistic collision operator is regularizing. This is a generalization of P. L. Lions’ analogous result in the nonrelativistic situation. The regularizing theorem has many applications in kinetic theory, and a few are discussed in this paper. In particular, the asymptotic behaviour of periodic solutions to the relativistic Boltzmann equation is studied. We show that such solutions converge strongly in

Existence of CMC and Constant Areal Time Foliations in T 2 Symmetric Spacetimes with Vlasov Matter

L^1

Existence of axially symmetric static solutions of the Einstein-Vlasov system

to a global Juttner equilibrium solution (sometimes called a relativistic Maxwellian) provided that the initial data satisfy the physically natural bounds of finite energy and entropy.

Bounds on M/R for static objects with a positive cosmological constant

Abstract The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a two-dimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the Einstein–Vlasov system when conformal or areal coordinates are introduced.

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.

Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant Λ, which are regular at the centre, and we investigate the influence of Λ on the bound of M/R, where M is the ADM mass and R is the area radius of the boundary of the static object. We find that for any solution which satisfies the energy condition p + 2p ⊥ ≤ ρ, where p ≥ 0 and p ⊥ are the radial and tangential pressures respectively, and ρ ≥ 0 is the energy density, and for which 0 ≤ ΛR 2 ≤ 1, the inequality holds. If Λ = 0, it is known that infinitely thin shell solutions uniquely saturate the inequality, i.e. the inequality is sharp in that case. The situation is quite different if Λ > 0. Indeed, we show that infinitely thin shell solutions do not generally saturate the inequality except in the two degenerate situations ΛR 2 = 0 and ΛR 2 = 1. In the latter situation there is also a constant density solution, where the exterior spacetime is the Nariai solution, which saturates the inequality; hence, the saturating solution is non-unique. In this case the cosmological horizon and the black hole horizon coincide. This is analogous to the charged situation where there is numerical evidence that uniqueness of the saturating solution is lost when the inner and outer horizons of the Reissner-Nordstrom solution coincide.